But, during the two-hour debate on tuition fees, Mr Wallace said immediate abolition "would remove millions of pounds from further and higher education and that was not part of our election manifesto," writes Neil Munro.
Mr Wallace's motion, setting up the promised committee of inquiry into fees and student financial support, was passed by 70 votes to 52. An amendment by John Swinney, deputy SNP leader, to abolish fees and establish an inquiry into student funding was defeated by 69 votes to 56.
Mr Swinney said an end to fees was "a matter of principle. It's a matter of free education not fee education, and it's a very Scottish principle."
Brian Monteith, Tory education spokesman, supported Mr Swinney and said the SNP amendment should appeal to Liberal Democrats since they would gain abolition and still have an inquiry.
Sylvia Jackson, Labour MSP for Stirling and a former Moray House lecturer, cautioned against abolition at the expense of higher education. "In helping students to pay the bill, we mustn't reduce the value of what they buy," she said.